What is the radius of the circle inscribed in a triangle whose sides are 4 cm, 7.5 cm and 8.5 cm?

Explanation

Check for right triangle: 4^2 + 7.5^2 = 16 + 56.25 = 72.25 = 8.5^2. This is a right-angled triangle. Its area is \frac{1}{2} \times 4 \times 7.5 = 15 sq cm. The semi-perimeter s = \frac{4 + 7.5 + 8.5}{2} = 10 cm. The inradius r = \frac{\text{Area}}{s} = \frac{15}{10} = 1.5 cm.

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